Cidofovir, an antiviral nucleoside analog, has been found to be effective in CMV retinitis due to AIDS. A devastating complication of HIV-1 is progressive multifocal leukoencephalopathy (PML). PML is a demyelinating disease of the white matter of the brain caused by reactivation of theJC virus, a member of the papovavirus family. There is currently no known effective treatment of PML. Cidofovir has demonstrated in vitro activity against papovaviruses. This pilot study will attempt to demonstrate the safety, efficacy and tolerability of cidofovir in the treatment of HIV-1-associated PML. Secondary objectives will be to assess the effect of cidofovir on CNS lesions, and the amount of JCV DNA in the CSF and PBMCs of these patients.